Moving an f-curve from an object to a bone
Yes you can. The workflow would be:


Append the action;
Switch to Dope Sheet Editor (shortcut is ShiftF12), then change Editor Mode to Action Editor;
Select the appended action from the dropdown list in the header, select keys you want, then CtrlC (or click the second last button at the right-end of the header);
Select the target bone in Pose Mode, add necessary channels by keying if there isn't any yet. Make sure the cursor is at the expected position, select channels you want to add action on, then CtrlV to paste (or click the last button at the right-end of the header). You can also do this step in Graph Editor.


PS: 


The action can be transformed between objects and bones, as long as they got same channel types. However, the result may be not always as expected as you really want. 
One thing that you should be aware of is the consistency of the rotation mode. For example, if the action for the appended action uses rotation mode as XYZ Euler, and the bone uses Quaternion (WXYZ), then it will fail, either.